Question $7$ : If $\$ 8000$ is invested at a rate of $6 \%$ compounded continuously, find the balance in the account after $4$ years. Use the formula $P=P_{0} e^{r t}$ . Determine how many years, to the nearest year, it will take for his initial investment to tripled. $\newline$ ( $7$ points)

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Grade 8

Compound interest

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Q. Question

7

: If

\$ 8000

is invested at a rate of

6 \%

compounded continuously, find the balance in the account after

4

years. Use the formula

P=P_{0} e^{r t}

. Determine how many years, to the nearest year, it will take for his initial investment to tripled.

\newline

(

7

points)

Calculate Balance After $4$ Years: Use the formula $P = P_0 \cdot e^{rt}$ to find the balance after $4$ years. $P_0 = \$8000$ , $r = 6\%$ or $0.06$ , $t = 4$ years. Calculate $P = 8000 \cdot e^{0.06\cdot4}$ .
Find Investment Triple Time: $P = 8000 \times e^{0.24}$ . Use a calculator to find $e^{0.24}$ and multiply by $8000$ .
Find Investment Triple Time: $P = 8000 \times e^{0.24}$ . Use a calculator to find $e^{0.24}$ and multiply by $8000.e^{0.24} \approx 1.27124915032$ . $P \approx 8000 \times 1.27124915032$ .
Find Investment Triple Time: $P = 8000 \times e^{0.24}$ . Use a calculator to find $e^{0.24}$ and multiply by $8000.e^{0.24} \approx 1.27124915032$ . $P \approx 8000 \times 1.27124915032$ . $P \approx 10169.99320256$ . Round to the nearest cent. $P \approx \$(10170.00)$ .
Find Investment Triple Time: $P = 8000 \times e^{0.24}$ . Use a calculator to find $e^{0.24}$ and multiply by $8000$ . $e^{0.24} \approx 1.27124915032$ . $P \approx 8000 \times 1.27124915032$ . $P \approx 10169.99320256$ . Round to the nearest cent. $P \approx \$(10170.00)$ .Now, find how many years it will take for the investment to triple. Set $P = 3 \times P_0$ and solve for $t$ . $3 \times P_0 = P_0 \times e^{rt}$ . $e^{0.24}$ $0$ .
Find Investment Triple Time: $P = 8000 \times e^{0.24}$ . Use a calculator to find $e^{0.24}$ and multiply by $8000$ . $e^{0.24} \approx 1.27124915032$ . $P \approx 8000 \times 1.27124915032$ . $P \approx 10169.99320256$ . Round to the nearest cent. $P \approx \$(10170.00)$ .Now, find how many years it will take for the investment to triple. Set $P = 3 \times P_0$ and solve for $t$ . $3 \times P_0 = P_0 \times e^{rt}$ . $e^{0.24}$ $0$ .Take the natural logarithm (ln) of both sides to solve for $t$ . $e^{0.24}$ $2$ . $e^{0.24}$ $3$ .
Find Investment Triple Time: $P = 8000 \times e^{0.24}$ . Use a calculator to find $e^{0.24}$ and multiply by $8000$ . $e^{0.24} \approx 1.27124915032$ . $P \approx 8000 \times 1.27124915032$ . $P \approx 10169.99320256$ . Round to the nearest cent. $P \approx \$(10170.00)$ .Now, find how many years it will take for the investment to triple. Set $P = 3 \times P_0$ and solve for $t$ . $3 \times P_0 = P_0 \times e^{rt}$ . $e^{0.24}$ $0$ .Take the natural logarithm (ln) of both sides to solve for $t$ . $e^{0.24}$ $2$ . $e^{0.24}$ $3$ . $e^{0.24}$ $4$ is $e^{0.24}$ $5$ , so $e^{0.24}$ $6$ . $e^{0.24}$ $7$ .
Find Investment Triple Time: $P = 8000 \times e^{0.24}$ . Use a calculator to find $e^{0.24}$ and multiply by $8000$ . $e^{0.24} \approx 1.27124915032$ . $P \approx 8000 \times 1.27124915032$ . $P \approx 10169.99320256$ . Round to the nearest cent. $P \approx \$(10170.00)$ . Now, find how many years it will take for the investment to triple. Set $P = 3 \times P_0$ and solve for $t$ . $3 \times P_0 = P_0 \times e^{rt}$ . $e^{0.24}$ $0$ . Take the natural logarithm (ln) of both sides to solve for $t$ . $e^{0.24}$ $2$ . $e^{0.24}$ $3$ . $e^{0.24}$ $4$ is $e^{0.24}$ $5$ , so $e^{0.24}$ $6$ . $e^{0.24}$ $7$ . Use a calculator to find $e^{0.24}$ $8$ and divide by $e^{0.24}$ $9$ . $8000$ $0$ . $8000$ $1$ .
Find Investment Triple Time: $P = 8000 \times e^{0.24}$ . Use a calculator to find $e^{0.24}$ and multiply by $8000.e^{0.24} \approx 1.27124915032$ . $P \approx 8000 \times 1.27124915032$ . $P \approx 10169.99320256$ . Round to the nearest cent. $P \approx \$(10170.00)$ . Now, find how many years it will take for the investment to triple. Set $P = 3 \times P_0$ and solve for $t$ . $3 \times P_0 = P_0 \times e^{rt}$ . $3 = e^{0.06t}$ . Take the natural logarithm (ln) of both sides to solve for $t$ . $e^{0.24}$ $1$ . $e^{0.24}$ $2$ . $e^{0.24}$ $3$ is $e^{0.24}$ $4$ , so $e^{0.24}$ $5$ . $e^{0.24}$ $6$ . Use a calculator to find $e^{0.24}$ $7$ and divide by $e^{0.24}$ $8$ . $e^{0.24}$ $9$ . $8000.e^{0.24} \approx 1.27124915032$ $0$ . $8000.e^{0.24} \approx 1.27124915032$ $1$ . Round to the nearest year. $8000.e^{0.24} \approx 1.27124915032$ $2$ years.